Multi-target Tracking Using Wireless Sensor

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Multi-target Tracking Using Wireless Sensor Networks Based on Higher-Order Voronoi Diagrams Manel Abdelkader, Mohamed Hamdi, and Noureddine Boudriga Communication Networks and Security Research Lab. University of November 7th at Carthage, Tunisia Email: [email protected],{nab, nab}@supcom.rnu.tn

Abstract— Recent advances in integrated electronic devices motivated the use of Wireless Sensor Networks (WSNs) in many applications including target surveillance and tracking. A number of sensor nodes are scattered within a sensitive region to detect the presence of intruders and forward subsequent events to the analysis center(s). Obviously, the sensor deployment should guarantee an optimal event detection rate. This paper proposes a tracking framework based on Voronoi tessellations. Two mobility models are proposed to control the coverage degree according to target presence. The objective is to set a non-uniform coverage within the monitored zone to allow detecting the target(s) by multiple sensor nodes. We show how the proposed algorithm adapts to the situation where multiple targets move in the monitored zone. Moreover, we introduce an algorithm to discover redundant nodes (which do not provide additional information about target position). This algorithm is shown to be effective in reducing the energy consumption using an activity scheduling approach. Simulations are carried out to underline the efficiency of the proposed models.

I. I NTRODUCTION Wireless Sensor Networks (WSNs) are being used in many sensitive applications including mobile target tracking. Such applications are typically used in the military context to detect, analyze, and predict the movement of hostile vehicles. The primary criteria for assessing the efficiency of a WSN-based tracking framework is area coverage. In fact, the deployed sensors should cover, as long as needed, a maximum area of the monitored region. However, the nature of the monitored environment introduces some constraints to the WSN modeling problem. Effectively, the deployment of sensor nodes in a military environment can not be performed according to a deliberate choice. Due to the hostility of the physical environment, human control of sensor node localization is unfortunately impossible. Typically, sensor nodes are dropped from unmanned aircrafts in a specific area. The only parameter that can be effectively monitored is the sensor node density (number of nodes by unity of surface). This problem can be coped with by implementing mobility and activity scheduling strategies in order to guarantee an optimal scattering of the sensor nodes. In other terms, the sensor density (i.e., number of deployed © 2009 ACADEMY PUBLISHER doi:10.4304/jnw.4.7.588-597

sensors per unit of surface) does not vary from one portion of the monitored region to another. Very few works have addressed mobility and coverage in WSNs [1]. However, they fail in tracking multiple targets moving within the monitored zone. In this paper, we propose mobility and activity scheduling techniques for non-uniform area coverage. We extend our previous work [2] where the basic idea is that the sensor density should vary from a location to another according to the probability of presence of a hostile target. Effectively, the coverage degree should be increased in zones where the target is supposed to be. To implement this concept, we use Voronoi tessellations which serve to classify the points of the monitored zone according to their proximity to the sensor nodes. We present two mobility models. An advanced model providing an accurate estimation of the target position and a basic model which is less precise than the aforementioned one. Nonetheless, it is much less energy-consuming. Moreover, we introduce a new approach to discover redundant nodes (i.e., nodes that do not provide additional information with respect to their neighbors) and turn them off for a period of time. This can be useful in controlling the energy consumption of the network without altering its performance. The rest of the paper is structured as follows. Section II highlights the major WSN issues that will be covered in the paper. The basic assumptions of our work are given in Section III. Section IV provides the fundamental aspects of Voronoi diagrams. In Section V, we come up with two Voronoi-based mobility models. Section VI extends these models to multi-target tracking. Section VII introduces a redundancy discovery technique to reduce the network energy consumption. Simulations are carried out in Section VIII to assess the efficiency of the proposed approaches. Finally, Section IX concludes the paper.

II. WSN E NGINEERING In this section, we introduce the main engineering topics coping with WSNs. Then, we present an overview of the main related works that have been proposed in the literature.

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A. WSN Engineering Issues When conceiving a WSN network, three main issues should be defined. The first deals with coverage control while the second copes with mobility and the third is related to activity scheduling. These issues are narrowly related to target tracking. To maximize the control of a given area, sensors distribution should guarantee the coverage of the whole area. Thus, generally sensors are uniformly spread to ensure the detection of any target presence. Nevertheless, sensors are prone to multiple threats endangering their normal functioning and the accuracy of their detection information. In fact, sensors may be subject to environmental or security attacks leading to their deficiency or disability. Even more, they may be exploited to generate erroneous detection information. A mundane solution will be to increase the number of sensors, to correlate the detection signals and so to maximize the probability of an accurate detection. However, this may induce high investment with inefficient resource consumption, especially in zones not including a target. Further, this may overload the backbone with the process of useless detection signals. The best approach is to maximize sensors deployment in the target’s zones of presence. Effectively, it is more beneficial to increase the number of sensors only in the zones probably containing a target. These zones will be covered simultaneously by k sensors and are called k-covered zones. Figure 1 illustrates the k-coverage concept. The challenge for the backbone is to set the optimized parameter k ensuring the correctness of the detected signals. The definition of such non-uniform coverage affects sensors mobility and scheduling especially with the presence of multiple targets.

distinguished. The third important topic with regard to WSNs is activity scheduling which is important for sensor usage and target detection optimization. In fact, sensors are characterized by restricted physical constraints limiting the network lifetime. Thus, to maximize this lifetime, an adequate management model should be defined so that sensors are only used when there is a real need related to a target presence. A common approach is to program sensors activity according to the coverage ratio and targets presence. In the next subsection we provide a survey of the main techniques developed for multi-target tracking in wireless sensor networks. B. Multi Target Tracking in WSN networks Multi-target tracking (MTT) is not a trivial extension of single target tracking. The main problem related to this kind of tracking is data association. In fact, detection signals should be accurately assigned to the relevant sensors. For multi target tracking, two main approaches were defined: centralized tracking and distributed tracking. The first is characterized by its high computational complexity due to the size of all possible target trajectories and the need to increase sensing dimensional space. The second approach relies on the simultaneous usage of the computational resources available in the distributed sensors. Thus, additional constraints related to resources limitations are known. Different approaches coping with maximizing sensors usefulness while addressing complexity issues were presented. The tracking problem can be formulated as the need for obtaining an estimate of the target state from a measurement history. Two main techniques address this target tracking estimation. The first is sequential Bayesian filtering where tracking is ensured as follows Z t t t t p(x |z ) ∝ p(z |x ). p(xt |xt−1 ).p(xt−1 |z t−1 )dxt−1 ; χ

Figure 1. Higher-order coverage.

Following the initial distribution, sensors moves whether voluntarily or not. An uncontrolled mobility may lead to the non-coverage of certain zones while a controlled mobility may threaten sensors and the detection information. Consequently, mobility decision should be mostly made by sensors at the ground layer. Nevertheless, this may lead to unequal sensors distribution and information loose. Thus, the challenge is to define an optimized mobility model guaranteeing sensors security and network control. This becomes more challenging when multiple targets should be tracked. In fact, sensors positioning should guarantee the coverage of all targets. In addition, the detection signals related to each target should be © 2009 ACADEMY PUBLISHER

(1) where the current filter distribution p(xt |z t ) is computed from the previous filter distribution p(xt |z t−1 ) and the new observation z t . MTT is formulated as a sequential Bayesian filtering problem of a Markov process with noisy measurements. In the following, we present a survey of the main approaches treating multi target tracking defined in the literature. The two first are the predominant traditional approaches. Multiple hypothesis tracking (MHT) relies on the definition of all possible associations of measurements to tracks and false alarms while respecting the mutual exclusion association constraint [5]. Data association decisions are delayed until sufficient data is received. MHT can address low detection probability, high false alarm rates, initiation and termination of tracks, and delayed measurements. However, it suffers from large storage space requirements and exponentially increasing processing. For particle implementation, hypothesis should be processed taking into account similarities and mistakes[6].

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The joint probabilistic data association filter (JPDAF) is based on the update of each individual track state with weighted combinations of all measurements [7]. Consequently, measurement association probabilities should be computed with respect to the mutual exclusion constraint. However, the number of targets needs to be initially known. III. BASIC ASSUMPTIONS The approaches we present in this paper are developed under the following assumptions: 1) Mobile nodes are equipped with binary sensors characterized by a sensing radius Rsi for a sensor si . Such sensors simply indicate whether a target is within their sensing range 2) The sensing range of a sensor s is a perfect disc denoted by Γ(s, Rs ) 3) The communication range is greater than the sensing range In addition, we consider the WHOMoVeS framework introduced by the authors in [4] as a heterogeneous sensor network composed of: • Ground sensors (gSs): are responsible for detecting targets moving in their sensing range and for ensuring individual functions assigned by upper layer. • Intermediate ground sensors (ISs): belong to the sensing layer but they are assigned more management and communication functionalities. They cope with nodes belonging to two WSN layers. From one hand, they are responsible of ground sensor coordination, job assignment and received messages handling and transmission to upper layer. From another hand, they allow interactions and coordination between the sensing and the core layers. Thus, intermediate ground sensors receive the instructions and the requests of the core layers and are in charge of their processing according to their available resources (i.e. ground sensors). • Core sensors: are part of the core sensing layer. They play a double-role in the described infrastructure. First, they are the direct “supervisors” of the sensing layer with regard to set of functions such as mobility, coverage and security. Second, they provide resources to perform other functions like imagery for satellites. • Satellites: are responsible of the initiation of a set of functions demanded by the control center including target tracking which may be based on image sequences. All results/outputs sent by the core layer are processed before their transmission to the requester at the control center (3D-image processing, target tracking results). • Control center: requires service, manages input parameters (location, kind of detection, kind/number of images), receives results for further analysis. In addition, it defines the kind of reactions to be taken, makes decisions, and sends orders to be applied © 2009 ACADEMY PUBLISHER

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through the exploitation of the presented architecture. Accurate tracking and long network lifetime are achieved through a strong cooperation between those layers. According to this reasoning, the process of acquiring and analyzing data related to mobile targets in the battlefield includes five steps as illustrated in the following: 1) Ground sensors detect the presence of a hostile target in the monitored field. They send their detection signals to the nearest intermediate sensor. The latter gathers all detection signals and send them to the core sensing layer.Satellites contacts periodically the core sensor layer to retrieve the detected signals. 2) The satellite contacts the Uninhabited Aerial Vehicles (UAVs) to acquire image data about the scene where the intrusion has been detected. 3) The UAVs gather image data through the embedded imaging sensors. 4) The UAVs establish connections with the satellite communication backbone in order to transmit highquality multimedia data about the battlefield. 5) Images related to multiple intrusion events are forwarded through the broadband satellite backbone to the analysis center where advanced tracking functionalities are carried out. IV. C OMPUTING H IGHER - ORDER VORONOI TESSELLATIONS

The objective of this section is to provide a tool for accurately gauging the coverage degree of the monitored zone. To this purpose, we rely on higher-order Voronoi diagrams [5]–[7] to determine the sub-regions that do not satisfy the k-coverage requirement. This concept has been essentially used to model robot motion planning [8], [9]. First, we give a mathematical representation for higher order Voronoi tessellation, which is a set of Voronoi cells. Then, a parallel calculation framework allowing an efficient computation of this tessellation is provided. A. Mathematical modeling of higher-order Voronoi diagrams We start by the definition of the mathematical model related to sensor nodes distribution. We identify the groups of the k-nearest neighbors using the higher order Voronoi model. Let M be a metric space; δ : M×M → R denoting the Euclidean distance on M. We denote by R = {pi , 1 ≤ i ≤ N } ⊆ M , a set of N sensor nodes having their coordinates in M. The Voronoi diagram associated to R is the unique subdivision defined in M such that every part of the subdivision contains the nearest neighbors defined in M for pi , 1 ≤ i ≤ N , in R. Every subdivision part is named a Voronoi Cell related to pi , 1 ≤ i ≤ N , and is determined using the following process.

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For every pi , pj ∈ R , we denote by H(pi , pj ) the half plane containing pi : H(pi , pj ) = {x ∈ M/δ(pi , x) < δ(pj , x)} .

(2)

It can be noticed that H(pi , pj ) is the half plane delimited by the bisector of line segment [pi , pj ] and including pi . The Voronoi cell related to pi is generated by the definition of the common area between all half-planes defined above and containing pi . Therefore, a Voronoi cell related to pi is expressed by: \ H(pi, pj ). (3) VR (pi ) = pj ∈R\{pi }

In our work, we are rather interested in partitioning M into isotopic cells according to k-nearest neighbors for a given distribution of pi , pj ∈ R. Starting from (k) a given sensor distribution, we search the set Pi = {pi1 , . . . , pik } containing the nearest sensor neighbors. Such groups can be obtained using the higher order-k Voronoi Diagram. The latter allows defining subsets of (k) M containing the nearest elements to Pi . This can be performed by finding the elements which are closer (k) to the most distant neighboring of Pi than any other (k) pj ∈ / Pi . As for the order-1 voronoi cells, an order-k cell is constructed using bisectors between its generators (k) and T the remaining of the metric space. V (Pi ) = (k) [H(pi1 , pj ) ∩ . . . ∩ H(pik , pj )] . The resulting pj ∈R\P i

(k)

Voronoi diagram is represented as Vk (S) = ∪∗ V (Pi ), Rk

where Xk∗ , for a set X, is the set of subsets having cardinality k. We also denote the set of neighbors of a point pi in a Voronoi tessellation V (P ) by N (pi , V (P )). B. Building higher-order Voronoi diagrams Many algorithms have been proposed in the literature to determine the Voronoi diagram for a set of points in a 2-D space. These approaches have been extended to the construction of higher-order Voronoi diagrams. In this section, we define the k-Voronoi diagram construction model which is based on the cooperation of R elements. In the following, we present the construction k-Voronoi diagram construction algorithm. Our strategy is based on the PRAM algorithm proposed in [10]. Its major merit is that it sets a computational cooperative framework to build k-Voronoi diagrams. The algorithm is run in a recursive manner in such a way that the (k − 1)-Voronoi diagram is used to compute the k-Voronoi diagram. A simplified description of this algorithm is given in Algorithm IV-B where every sensor node present in the sensor layer knows its“direct” neighbors (defined in its detection coverage or given by a core sensor). C. Higher-order Voronoi Diagram Deployment in WSN Engineering In the frame of our work, we deploy higher-order Voronoi diagrams for WSN engineering. In the following, © 2009 ACADEMY PUBLISHER

Algorithm 1 PRAM Algorithm Input:A set R of planar sensors, voronoi of order k − 1. Output: the Voronoi diagram of order k. (k−1) 1) Subdivide each region rik−1 induced by Pt ⊂R (k−1) into subregions according to V1 (RPt ) 2) Merge equivalent new subregions relevant to neighboring rik−1 . 3) Delete old edges and save the new vertices and edges of each rik0 .

we show how higher order Voronoi diagrams may be used to control coverage as well as sensors mobility and activity scheduling. Through the definition of sensors nearest zones and knowing the detection range of each sensor, coverage may be deduced. Simple Voronoi diagrams allow the definition of the nearest set of points to each sensor and so the deduction of the covered and the uncovered regions. Higherorder diagrams increase the coverage range through the definition of the nearest regions to a number k of sensors. This generalization allows the definition of k-coverage and so coverage range customization. In fact, coverage range should be increased in the probable target zones of presence and reduced in the remaining zones. This may have an influence on sensors mobility and activity scheduling. By this manner, we show in this work how we can exploit higher-order Voronoi diagrams to determine the zones of priority towards which a sensor should move. Priority is determined according to the coverage range of the current and the future estimated targets locations. Further, we use Voronoi to schedule sensors activity and optimize energy consumption. In fact, sensors are alternatively activated according to the need for higher coverage. V. A k-VORONOI - BASED MOBILITY MODEL In this section, we show how higher-order Voronoi diagrams can be used to implement sensor mobility modeling. We consider two mobility models. The first is an advanced model in which sensor nodes move toward regions where the hostile target is supposed to be. The second relies on estimating the uncovered zones within a Voronoi cell and moving sensor nodes toward the ’most uncovered region’ A. Advanced mobility model Obviously, the first model is more energy-consuming since it encompasses the prediction of the target position. Therefore, we suppose that the second model can be used when energy resources become scarce. The performance of both models will be assessed in the following sections. Moreover, the prediction function is tightly related to the coverage of the studied zone. In fact, the greater is the number of target detection signals, the better is the prediction precision. In the following, we distinguish

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both cases of a target crossing a k−covered and a non k−covered zone. For a target crossing a k−covered zone: The mobility algorithm is triggered upon the detection of a target presence. Every ground sensor sends his detection signal to the relevant intermediate sensor. The latter collects all detection signals, verifies their integrity and defines the zones that might include the target. The set of defined zones are classified according to the probability of presence of the target. This probability reaches his maximum when a zone is k−covered. The mobility algorithm is defined as follows: 1) The nearest k sensors si , 1 ≤ i ≤ k, send their detection signals to their intermediate sensors. 2) In the case where detection signals are sent to different intermediate sensors, the latters coordinate to gather all signals at the IS with the highest number of detection signals. 3) IS verifies the k−security of the received signals and constructs the zone of presence of the target zt . a) Let’s di be the detection signal of the sensor p si . di = (rti , αti , θti , si ) where (xsi − xti )2 + (ysi − yti )2 , αti = rti = −1 ysi −yti tan ( xs −xt ), θti is the detection instant. i i For every si , IS computes detection zone R αti +δα R the rti +δr zi such that zi = αti −δα rti −δr dαdr where δα, δr are the estimated detection error. The total target presence zone is resulted from the intersection between all the elementary detection zones. Thus, zt = ∩ zi 1≤i≤k

4) IS defines ∆Z as the zone surrounding zt and that a target can not go beyond in the next mobility step. IS computes the intersection between ZT = zt + ∆Z and the k−Voronoi diagram: (k) (k) (k) ∪ (ZT ∩ V (Pi )) = ∪ δVi , where δVi ⊆ i

(k)

∈Sk∗ (k) Vi (Pi ) pi

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detection signals received by the IS and k is the minimum required number of signals. 2) IS defines the nearest k sensors to each part of the zone zi . Thus, IS defines the intersection between zi (k) and the k−Voronoi diagram and deduces ∪ δVi . i

(k)

3) For each δVi , IS ascertain the sets of the nearest ksensors, verifies which sensors ki ”, 0 ≤ ki ” ≤ (k) k 0 , have sent detection signals. IS classifies δVi according to the value of ki ”. The greater ki ” is, the most important is the probability of presence of (k) the target in δVi . A small value of kj ” induces (k) that the target is going in or out δVj . (k) 4) For each δVi , IS guides the (k − k”) nearest (k) sensors to move towards δVi . For that, he sends them the mobility instruction including the probability of presence of a target A mobility instruction is defined as.(ri , αi , pi ) where ri ≥ d(si , p) such (k) that ∃ p, ∀q ∈ δVi , d(si , p) ≥ d(si , q). and αi = argmaxxs d i y where x, y ∈ vi and vi is the set of the vertices of δVi , pi = k”/k is the probability of (k) presence of the target in δVi . To enhance coverage while keeping more mobility freedom, we suggest a group mobility model in which ground sensors move in groups such that they preserve a k−coverage. For this purpose, for each mobility step, sensors define randomly groups of k members for each, the latters are not required to be the nearest neighbors. Each group defines randomly a head which chooses the first mobility step. The remaining members of the group take into account this choice to determine, in turn, their next mobility step. By this manner, each sensor’s mobility step depends on his integrating group. Further, a sensor may move from one group to another in each mobility step. This model enables the definition of overlapping k−Voronoi groups which increases the guarantee to have a k−coverage.

(k) Vi (Pi )

such that is the Voronoi cell of the k−sensors with index i. (k) 5) To guarantee k−coverage in ZT , each δVi (k) should be k−covered which means that δVi ⊂ ∩ Γ (sj , Rs ). 1≤j≤k

6) A mobility instruction is defined by (ri , αi ) where (k) ri ≥ d(si , p) such that ∃ p, ∀q ∈ δVi , d(si , p) ≥ d(si , q). and αi = argmaxxs d i y where x, y ∈ vi and vi is the set of the vertices of δVi . For a target crossing a non k−covered zone: In this case, only k 0 signed detection signals are retrieved by the intermediate sensors. IS proceeds at the construction of the probable zone of presence of the target as presented previously. In the same time, in order to refine the target presence zone, IS starts the recovery of the remaining (k − k 0 ) required signals. For this purpose, IS proceeds as follows: 1) let’s zi be a probable zone of presence of a target, pi be the probability of presence of a target where pi = ki /k such that ki is the number of the verified © 2009 ACADEMY PUBLISHER

B. Simplified mobility model We propose a mobility model which is only based on the Voronoi diagram. The following proposition gives a condition for a Voronoi cell to be partly uncovered. Proposition 5.1: Let S be a set of sensor node positions and si in S be a sensor node. If there exists nj in N (si , V (S)) such that d(si , nj ) > 2Rsi then V (si ) is not fully covered. Proof: We suppose that d(si , nj ) > 2Rsi . Let [vp , vq ] be the Voronoi edge defined by nj and si . The intersection of [vp , vq ] and [si , nj ] is denoted by P . The properties of the Voronoi diagram give that: d(si , P ) = d(nj , P ) =

d(si , nj ) . 2

(4)

Since d(si , nj ) > 2Rsi , we deduce from Equation 4 d(si , P ) > Rsi . Consider the point Q ∈ [si , P ] such that d(si , Q) = Rsi . We can conclude that for every T ∈ [P, Q], T ∈

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V (si ) and T ∈ / Γ(si , Rsi ) (because d(si , T ) > Rsi ). This means that V (si ) is not totally covered. This result can serve to implement a mobility algorithm where a sensor node looks for one or more neighbors that are at least 2Rsi -distant from it. If such nodes exist, the sensor node moves toward the most distant neighbor, d(si ,nf )−2Rsi . Figure 2 denoted by nf , with a distance 2 illustrates this reasoning. In fact, we notice that the disc centered in s1 and having a radius equal to Rsi does not cover the Voronoi cell generated by s1 . Hence, s1 will move toward s3 with a distance d(Q, P ).

Figure 2. Simplified mobility model.

The following corollaries extend this strategy to the case where the monitored region is required to be kcovered. For the sake of parsimony, we do not provide proofs for these corollaries in this paper. Corollary 1: For si in S, if |N (si , V (S))| < k, where |.| denotes set cardinality, then V (si ) is not k-covered. Before giving the second corollary, we define, for a sensor node si in S, the set X(si , V (S)) of intersection points expressed as follows: \ X(si , V (S)) = V (S^ \ {si }) Γ(si , Rsi ), (5) where Pe, for P ∈ R2 denotes the boundary of P . Informally speaking, X(si , V (S)) denotes the intersection of edges of the Voronoi diagram V (S \ {si }) and the disk corresponding to the maximum sensing coverage range of si . Corollary 2: For si in S, if |X(si , V (S))| < k, then V (si ) is not k-covered. The major advantages of these results is that we can rely on simple Voronoi diagrams to deal with k-coverage while the advanced model proposed in the previous subsection is based on k-Voronoi tessellations which are more complex to build. A more accurate comparison between the two models will be carried out in the simulation section. C. Group mobility modeling To enhance coverage while keeping more mobility freedom, we suggest a group mobility model in which ground sensors move in groups such that they preserve k-coverage. To this purpose, for each mobility step, © 2009 ACADEMY PUBLISHER

sensors define randomly groups of k members for each which are not required to be the nearest neighbors. Each group has a leader which defines mobility steps. The remaining members of the group take into account this choice to determine, in turn, their next mobility step. By this manner, each sensor’s mobility step depends on his integrating group. Further, a sensor may move from one group to another in each mobility step. This model enables the definition of overlapping k-Voronoi groups which increases the guarantee to have a k-coverage. Thus, in the aim to guarantee k-coverage all along the estimated target path, the following model is defined: • A group leader is elected from the set of the nearest nodes to the estimated target path and after receiving a mobility instruction. The group leader follows the mobility instruction sent by IS. Otherwise, groups will move away from the target path. • Each group leader is in charge of gathering group members. It searches increasingly in its neighborhood. • A member chooses to belong to a group as long as it does not receive a mobility instruction from an IS. Otherwise, a mobility instruction is prioritized. • For a mobility step, a member could only belong to a single group. It may then move to another group for further mobility steps. • A node may act as a group leader as long as it receives mobility instructions from the IS. VI. E XTENSION TO MULTI - TARGET TRACKING The advanced mobility model have defined the probable zones of a target presence and drives sensors towards these zones. Thus, a mobility instruction is clearly defined and weighted according to the probability of the target presence. In the case of multiple targets, a sensor may receive different mobility instructions and then it chooses which to follow. Nevertheless, this may lead to uneven sensors distributions. Hence, some targets may be not sufficiently covered especially when the number of sensors is not enough to cover all the targets’ estimated locations. For these reasons, we propose in the following two techniques enabling the extension of the advanced mobility model for multi-target tracking. To guarantee the coverage of multiple targets, we present the modifications introduced to the advanced mobility model. In the presented mobility model, sensors are free to define their next movement, two main situations may be defined. In the first one, sensors follow the mobility instruction driving to the target; so, they move towards the probable zones of target presence. In the second, a sensor chooses another different direction taking him away from these zones. The main idea introduced for multi-target tracking is that even when sensors are in the second situation, they remain in nearby locations increasing the probability to return to the target direction in next mobility steps. This can be fulfilled through the customization of velocity according to the chosen direction in the sense that sensor’s mobility velocity increases

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when sensors moves towards target location and inversely. For this reason, we define two velocity ranges. The first, denoted by {Vhi }, contains the high velocity values while the second, denoted by {Vli }, contains the low velocity values. The extended advanced mobility model links the sensor velocity to the chosen direction. Thus, mobility probability is defined as follows. • •

•

The probability that a node chooses a given velocity is equal to the probability to choose target direction. When receiving mobility instructions, the direction of the nearest targets have the higher probability. Consequently, they are assigned the higher probability velocity values. Three subsets of velocity values may be defined: (1) a velocity value Vt enabling the sensor to reach the target position in the next mobility step; (2) a velocity value from {Vhi } when choosing the target direction but not sufficient to reach the target; (3) a velocity value from {Vli } when choosing an other direction.

The underlying probability distribution is defined as follows:  v = Vt  P ((r, α) = (rt , αt )) 1 v ∈ {Vhi } P rV (v) = V¯hi P ((r, α) = (ri , αi ))   1 (1 − P ((r, α) = (ri , αi )) v ∈ {Vli } V¯li In the following, we divide the monitored zones into regions related to the present targets. Let T be the number of the tracked targets. In algorithm 2, we identify the nearest sensors to each target. Then, we move sensors such that target path remains k-covered.

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Definition 1: A sensor si ∈ S is said to be redundant if, and only if:  ∅ 6= Γ(si , Rsi )

\



Γ(sj , Rsj ) = Γ(si , Rsi ),

sj ∈Σ(si )

(6) where Σ(si ) = {s ∈ S : Γ(s, Rs ) ∩ Γ(si , Rs ) 6= ∅ ∧ s 6= si }. The interest, from the energy consumption optimization point of view, of identifying redundant sensors is obvious since such nodes can be turned-off. In fact, the information provided by a redundant sensor about the presence of a hostile target can be obtained from its neighbors. In the rest of the section, we look for a characterization of redundant sensor nodes. The following proposition gives a necessary and sufficient condition for node redundancy characterization. Proposition 7.1: Let S be a set of sensor node positions in R2 and X(si ) the set of intersection points corresponding to si ∈ S. If si is redundant if, and only if: [ Γ(sj , Rsj ). (7) X(si , V (S)) ⊂ sj ∈N (si ,V (S))

Proof: (i) Proof of ⇒: If a sensor si is redundant, it comes from Proposition 5.1 that: N (si , V (S)) ⊆ Σ(si ).

(8)

Therefore, it can be written that: [

Algorithm 2 Extended group mobility model for multitarget tracking While (number of sensors in target’s Delaunay triangle ¿ threshold) do Compute T -Voronoi where T is the number of targets Define the k-Voronoi in each T -cell Apply the group mobility model in each cell

 [

[

Γ(sj , Rsj ) ⊆

Γ(sj , Rsj ).

(9)

sj ∈Σ(si )

sj ∈N (si ,V (S))

From Equations 6 and 9, it comes that if si is redundant then  Γ(si , Rsi )

\



 [

Γ(sj , Rsj ) = Γ(si , Rsi ).

sj ∈N (si ,V (S))

VII. S ENSOR ACTIVITY SCHEDULING In this section, we highlight the potential given by Voronoi diagrams in implementing activity scheduling strategies. We mainly show how sensors that do not contribute effectively in enhancing the coverage degree within a given zone can be detected and therefore turnedoff for a laps of time. Our idea is to exploit the properties of the Voronoi tessellation to implement a distributed algorithm to identify sensor nodes which sensing coverage is already covered by their neighbors. We first give the definition of a redundant sensor. © 2009 ACADEMY PUBLISHER

Moreover, Equation 7 gives that X(si , V (S)) ⊂ Γ(si , Rsi ). By transitivity of the inclusion operator, we obtain: X(si , V (S)) ⊂

[

Γ(sj , Rsj ).

sj ∈N (si ,V (S))

(ii) Proof of ⇐: Trivial. According to the proposition above, if there exists xj ∈ X(si ) such that xj ∈ / Γ(si , Rsi ), then si is not redundant. Consequently, we propose an algorithm for stating whether a node is redundant or not.

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Algorithm 3 Redundant sensor discovery ∀si ∈ S { Compute N (si , V (S)); Generate V (N (si , V (S)) \ {si })); Compute X(si , V (N (si , V (S)) \ {si }))); ∀xj ∈ X(si , V (N (si , V (S)) \ {si }))) { r:=0; ∀sk ∈ N (si , V (S)) { if (xj ∈ / Γ(sk , Rsi )) then r:=1; } } if (r=1) then si is not redundant; else si is redundant; } The following corollary extend the result of Proposition 7.1 to the case where a k-coverage of the monitored zone is needed. Obviously, the definition of redundancy should be slightly modified in this case to encompass sensor nodes whose sensing coverage is totally k-covered. Corollary 3: Let si in S be a sensor node. ³For every xj in X(s , V (S)), if ´ i T S |{xj } sk ∈N (si ,V (S\{si }) Γ(sk , Rsi ) | < k, then si is not redundant. Using this corollary, the strategy defined in Algorithm VII remains effective in sensitive contexts where the monitored area should be k-covered. VIII. S IMULATIONS AND RESULTS The simulations described in this section have been performed using the Matlab environment. We limit our experiments to the random walk, random waypoint, random direction and Gauss-Markov mobility models [11]–[14]. For each model, movements are computed for a set of nodes characterized by a sensing range of 20m, a velocity range of [0, 10m/s], and moving in a region of area 300m x 300m during 500 seconds.

A. Assessing Voronoi-based Mobility strategies In this subsection we present the results of the simulations that have been conducted to assess the efficiency of the proposed mobility models. We rely on the ALUL (Average Linear Uncovered Length) metric (expressed in meters) which has been extensively used in the literature to estimate the efficiency of coverage approaches. It is based on estimating the average distance the target can make before being detected by the WSN. Figures 3 and 4 show that the Advanced Voronoi-Based Mobility Model (AVBMM) has the better performance among the tested models. The basic model (BVBMM) is also very efficient since it is outperformed only by DPRMM and AVBMM. From Figure 3, it comes that AVBMM allows a gain, in terms of ALUL, of 98% and 87% with respect to the Gauss-Markov and random direction models; respectively. In Figure 4, it can be noticed that, when the monitored area is 2-covered, the © 2009 ACADEMY PUBLISHER

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coverage quality obtained using Voronoi-based models introduce an enhancement of about 90% with regard to the other models. B. Complexity analysis of Voronoi-based redundancy detection In this subsection, we assess the complexity added by the discovery of redundant sensors based on Voronoi diagrams. We consider the three following metrics: • A1 : Number of operations needed to detect the target and forward the corresponding alerts without eliminating redundant sensors • A2 : Number of operations needed to compute the Voronoi diagram and discover redundant nodes • A3 : Number of operations needed detect the target and forward the corresponding alerts taking into consideration sensor redundancy • A4 : Number of operations needed to forward the target information to the control center Figure 5 shows that the redundancy detection strategy is more energy-effective since it requires less operations than the traditional tracking process. IX. C ONCLUSION This paper presented two Voronoi-based mobility models for target tracking using WSNs. The key advantage of

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these models is that they encompass the potential target position in the construction of the mobility instructions. This ensures that the locations where the target is most probable to be are more covered than the rest of the monitored area. We also proposed a redundancy discovery technique to enhance the WSN cost-effectiveness. An enhancement of this work to build a multi-target tracking framework is currently under development. R EFERENCES [1] W. Wang, V. Srinivasan, and K-C. Chua, ”Trade-offs Between Mobility and Density for Coverage in Wireless Sensor Networks,” MobiCom07, September 914, 2007, Montral, Qubec, Canada. [2] M. Abdelkader, M. Hamdi, N. Boudriga, ”Voronoi-based Sensor Network Engineering for Target Tracking Using Wireless Sensor Networks,” Workshop on Security of Wireless Communication Systems, IFIP NTMS Conference, Tangier, Morocco, Nov. 2008. [3] C. Gui and P. Mohapatra, Power Conservation and Quality of Surveillance in Target Tracking Sensor Networks, Proc. ACM MobiCom ’04, pp. 129-143, Sept. 2004. [4] M. Hamdi, N. Boudriga, M. S. Obaidat, ”WHOMoVeS: An optimized broadband sensor network for military vehicle tracking,” International Journal of Communication Systems, Vol. 21 , Issue 3, pp. 277-300, ISSN:1074-5351, 2008. [5] L. Wang, H. Shen, Z. Chen, and Y. Lin, ” Voronoi Tessellation Based Rapid Coverage Decision Algorithm for Wireless Sensor Networks,” Lecture Notes in Computer Science, Ubiquitous Intelligence and Computing, Springer, 2007. [6] I. Stojmenovic, A. K. Ruhil, D.K. Lobiyal, ” Voronoi Diagram and Convex Hull Based Geocasting and Routing in Wireless Networks ,” Proceedings of the Eighth IEEE International Symposium on Computers and Communication (ISCC03), KEMER - ANTALYA, Turkey, 2003. [7] Marcos Augusto M. Vieira, Luiz Filipe M. Vieira, Linnyer B. Ruiz, Antonio A. F. Loureiro, Antonio O. Fernandes, Nogueira Nogueira, ”Scheduling Nodes in Wireless Sensor Networks: A Voronoi Approach,” lcn, p. 423, 28th Annual IEEE International Conference on Local Computer Networks (LCN’03), 2003. [8] M. Seda, ”A Comparison of Roadmap and Cell Decomposition Methods in Robot Motion Planning,” WSEAS Transactions on Systems and Control, Vol. 2, Issue 2, 2007, pp. 101-108. [9] Roque, W. L. and Doering, D. 2005. Trajectory planning for lab robots based on global vision and Voronoi roadmaps. Robotica 23, 4 (Jul. 2005), 467-477.

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[10] H. Meyerhenke, ”Constructing Higher-Order Voronoi Diagrams in Parallel,” EWCG 2005, Eindhoven, March 911, 2005. [11] T. Camp, J. Boleng, and V. Davies, A Survey of Mobility Models for Ad Hoc Network Research, in Wireless Communication and Mobile Computing (WCMC): Special issue on Mobile Ad Hoc Networking: Research, Trends and Applications, vol. 2, no. 5, pp. 483-502, 2002. [12] B.Liang, Z. J. Haas, Predictive Distance-Based Mobility Management for PCS Networks, in Proceedings of IEEE Information Communications Conference (INFOCOM 1999), Apr. 1999. [13] L. Lima, J. Barros, ”Random Walks on Sensor Networks,” the 5th International Syposium on Modeling and Optimization in Mobile, Ad hoc, and Wireless Networks (WiOpt 2007), Limassol, Cyprus, April, 2007. [14] C. Bettstetter, G. Resta, and P. Santi, ”The Node Distribution of the RandomWaypoint Mobility Model for Wireless Ad Hoc Networks”, IEEE Transactions on Mobile Computing, Vol. 2, No. 3, pp. 257-269, July-Sept 2003. Manel Abdelkader Ms Manel Abdelkader received his Engineering Diploma and Master Diploma from the Engineering School of Communications (Sup’Com, Tunisia) on 2002 and 2004 respectively. From 2002 until now she is working for the National Digital Certification Agency (NDCA, Tunisia) where she is head of the Certification and PKI Unit. Ms. Manel is in charge to set the certification Policy for the Tunisian root Certification Authority. She is also serving in various national technical committees for securing e-government services. Currently, Ms. Manel is a PhD student at the Engineering School of Communications at Tunis. She is also member of the Communication Networks and Security Lab, where Ms. Manel is conducting research activities in security of grid architectures and wireless sensor networks.

Mohamed Hamdi received his Engineering Diploma, Master Diploma, and PhD in telecommunications from the Engineering School of Communications (SupCom, Tunisia) on 2000, 2002, and 2005; respectively. He is recipient of the Best Thesis Award from the Tunisian Telecommunications Scientific Society. From 2001 to 2005 he has worked for the National Digital Certification Agency (NDCA, Tunisia) where he was head of the Risk Analysis Team. Currently, Dr. Hamdi is serving as assistant professor for the Engineering School of Communications at Tunis. He is also member of the Communication Networks and Security Lab (Coordinator of the Formal Aspects of Network Security Research Team), where Dr. Hamdi is conducting research activities in the areas of risk management, algebraic modeling, relational specifications, intrusion detection, network forensics, and wireless sensor networks.

Noureddine Boudriga is an internationally known scientist/ academic. He received his Ph.D. in Algebraic topology from University Paris XI (France) and his Ph.D. in Computer science from University of Tunis (Tunisia). He is currently a Professor of Telecommunications at University of Carthage, Tunisia and the Director of the Communication Networks and Security Research Laboratory (CNAS) He is the recipient of the Tunisian Presidential award in Science and Research (2004). He has served as the General Director and founder of the Tunisian National Digital Certification Agency. He was involved in very active research and authored or coauthored many chapters and books. He published over 200 refereed journal and conference papers. Prof. Boudriga is the President of the Tunisian Scientific Telecommunications Society.